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If the price of sugar is increased by 10%, then by how much percent consumption should be reduced so that the expenditure remains the same?
- a)9.09
- b)10
- c)12.5
- d)20
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the price of sugar is increased by 10%, then by how much percent co...
Let the price be Rs. x /kg
Consumption be y kg
Expenditure = price × consumption
⇒ Expenditure = x × y
Price of sugar is increased by 10%
New price of sugar = 1.1 x /kg
Let new consumption be z kg
New Expenditure = (1.1x) × z
New Expenditure = old Expenditure
⇒ (1.1x) × z = x × y
⇒ z = y/1.1
Reduction in consumption = (y - z) = y - y/1.1 = y/11
Percentage reduction in consumption=(reduction in consumption/original consumption)× 100
Percentage reduction in consumption = [(y/11)/y] × 100 = 100/11 = 9.09%
Consumption be y kg
Expenditure = price × consumption
⇒ Expenditure = x × y
Price of sugar is increased by 10%
New price of sugar = 1.1 x /kg
Let new consumption be z kg
New Expenditure = (1.1x) × z
New Expenditure = old Expenditure
⇒ (1.1x) × z = x × y
⇒ z = y/1.1
Reduction in consumption = (y - z) = y - y/1.1 = y/11
Percentage reduction in consumption=(reduction in consumption/original consumption)× 100
Percentage reduction in consumption = [(y/11)/y] × 100 = 100/11 = 9.09%
Shortcut method :
If the price of a commodity increases by r%, then the reduction in consumption so as not to increase the expenditure = [r/(100 + r)] × 100%
If the price of a commodity increases by r%, then the reduction in consumption so as not to increase the expenditure = [r/(100 + r)] × 100%
Percentage reduction in consumption = [10/(100 + 10)] × 100 = 1000/110 = 9.09%
Most Upvoted Answer
If the price of sugar is increased by 10%, then by how much percent co...
Let's assume that the original price of sugar is $100 per unit and the original consumption is 100 units.
Step 1: Calculate the original expenditure:
Expenditure = Price * Consumption
Original Expenditure = $100 * 100 units = $10,000
Step 2: Calculate the new price after a 10% increase:
New Price = Original Price + (Original Price * Increase Percentage)
New Price = $100 + ($100 * 0.10) = $100 + $10 = $110
Step 3: Calculate the new consumption needed to keep the expenditure the same:
New Expenditure = New Price * New Consumption
New Expenditure = $110 * New Consumption
Since we want the new expenditure to remain the same as the original expenditure, we can equate the two:
$10,000 = $110 * New Consumption
Step 4: Solve for the new consumption:
New Consumption = $10,000 / $110
New Consumption ≈ 90.91 units
Step 5: Calculate the percentage reduction in consumption:
Reduction Percentage = (Original Consumption - New Consumption) / Original Consumption * 100%
Reduction Percentage = (100 units - 90.91 units) / 100 units * 100%
Reduction Percentage ≈ 9.09%
Therefore, the consumption should be reduced by approximately 9.09% in order to keep the expenditure the same when the price of sugar is increased by 10%.
Hence, the correct answer is option A) 9.09.
Step 1: Calculate the original expenditure:
Expenditure = Price * Consumption
Original Expenditure = $100 * 100 units = $10,000
Step 2: Calculate the new price after a 10% increase:
New Price = Original Price + (Original Price * Increase Percentage)
New Price = $100 + ($100 * 0.10) = $100 + $10 = $110
Step 3: Calculate the new consumption needed to keep the expenditure the same:
New Expenditure = New Price * New Consumption
New Expenditure = $110 * New Consumption
Since we want the new expenditure to remain the same as the original expenditure, we can equate the two:
$10,000 = $110 * New Consumption
Step 4: Solve for the new consumption:
New Consumption = $10,000 / $110
New Consumption ≈ 90.91 units
Step 5: Calculate the percentage reduction in consumption:
Reduction Percentage = (Original Consumption - New Consumption) / Original Consumption * 100%
Reduction Percentage = (100 units - 90.91 units) / 100 units * 100%
Reduction Percentage ≈ 9.09%
Therefore, the consumption should be reduced by approximately 9.09% in order to keep the expenditure the same when the price of sugar is increased by 10%.
Hence, the correct answer is option A) 9.09.
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